For the briefest of moments, the Jets’ fans liked what they saw from Mark Sanchez, the target of so much vitriol over the past year.

Sanchez, on Jacksonville’s 5-yard line last night, threw the ball away during a collapsing play – an encouraging change from the Jets’ preseason opener in Detroit, where Sanchez forced a throw under pressure that was returned 14 yards for a touchdown.

That foible came on Sanchez’s first possession in Detroit. He opened last night by leading the Jets on a six-play, 59-yard touchdown drive. Nary a boo was heard in MetLife Stadium – a stark contrast to late last season, when the masses shredded Sanchez.

Sanchez’s second drive last night was productive, too, as the Jets moved 53 yards and got a field goal. This was Sanchez’s evening alone in his protracted quarterback competition with rookie Geno Smith, who sat out last night with a sore right ankle. And Sanchez seemed intent on owning the moment, in a game the Jets would win 37-13.

The crowd actually cheered his throw-away from the 5 during his third possession, however sarcastic the applause might have been. Two plays later, Sanchez faced third down and 3 from the 3. He looked for tight end Kellen Winslow in the crowded end zone, and tried to sneak a throw in. But cornerback Marcus Trufant intercepted in.

In an instant, Sanchez’s fleeting good will was gone. The fans groaned. They shook their heads. They booed.

After the Jets punted, Sanchez had a prime scoring chance on his fifth and final possession of the half. The Jaguars botched the punt return, and the Jets took over at Jacksonville’s 3 with 24 seconds left. Even this Jets offense, thin on talent, could score a touchdown from here, right?

Nope.

Eschewing a field goal, the Jets lined up for third and goal from the 6 with six seconds left. Before the play, right tackle Austin Howard waved his arms to encourage the fans. Sanchez took the snap and scrambled. The clock ticked. Nobody was open. Sanchez didn’t throw the ball away. He kept rolling out. Sanchez threw to the side of the end zone. The ball sailed wide. No time was left. The fans booed.

That play and the pick significantly marred an otherwise solid performance by Sanchez – on a rinse-and-repeat night for the fifth-year pro. Sanchez played three quarters and completed 13 of 23 passes for 169 yards, one touchdown and one pick. He came out with the second-team offense in the second half, after playing with the starters in the first half, when he was 8-of-14 passing for 82 yards, with the touchdown and interception.

Afterward, Jets coach Rex Ryan shouldered blame for the risky call to end the half. Sanchez did the same, for his role in the play, which wasn’t a designed rollout.

“That won’t happen again,” Sanchez said. “That shouldn’t happen. I’ve got to get rid of that ball sooner and not scramble. I know better than that.”

Sanchez’s smart throw-away accounted for one of his six incomplete passes in the first half. He saw three other passes bounce off the hands of Stephen Hill, Clyde Gates and Jeremy Kerley (in the end zone on the first half’s second-to-last play). Then there was the interception, and the mental lapse to end the half.

So the beat goes on with Sanchez-Smith – a race to the Sept. 8 season opener that began in the spring, and still isn’t resolved, with the first game three weeks from today.

“I feel like, with Geno not playing, this was going to go on until he got another shot, I’m sure,” Sanchez said.

The Jets’ coaches have emphasized the importance of limiting turnovers this preseason, and even though Sanchez now has 20 picks in his last 17 games since the start of the 2012 regular season, Smith can’t gain ground from the sideline.

Ryan said the team and its medical staff opted not to play Smith because “there’s a big difference in being in a red (non-contact) jersey (in practice) and being protected that way than there is being in a green-and-white jersey with live action coming at you.”

But now, Smith could be running out of time to win the job. The Jets resume practice tomorrow. If Smith returns then, he will have had four days to rest his ankle.

“I’m going to go out there with the right mentality and try to win the job,” he said. “Right now I’m feeling good. I’m eager to get to next week and start things rolling.”

The Jets’ third of four preseason games is Saturday night against the Giants. Sanchez started against Detroit, and Smith played three and a half series before getting hurt. New offensive coordinator Marty Mornhinweg said he wasn’t able to get a complete evaluation of Smith from the game because he wanted to examine other players in specific scenarios when Smith was on the field.

The Jets hoped last night would provide a chance to get a better look at Smith. But they now find themselves still waiting for that opportunity, and still seeing more of the same.